This electromagnetic interference, as is known, is in particular generated by the electric motor of such a vehicle.
A radio receiver, in particular in a multimedia system of a motor vehicle, is able to receive a radio signal, in particular an AM radio signal. Electromagnetic interference is generated by the motor of such vehicles, in particular the electric motor of an electric or hybrid vehicle, which perturbs the reception of the AM radio signal.
To remove this electromagnetic interference, it is known in the art to make use of filters implementing iterative algorithms, which algorithms are referred to as CPA algorithms, CPA standing for “Constant Phase Algorithm”. As their name indicates, these CPA algorithms aim to ensure the processed AM radio signal has a constant phase.
More precisely, CPA algorithms are used to define the best filter to apply to the received AM radio signal, with a view to removing the electromagnetic interference therefrom.
Such an AM radio signal, received in modulated form by a radio receiver, is subjected to various sensors and to suitable filtering so that the corresponding demodulated radio signal is able to be played back under good conditions, in particular in the passenger compartment of a motor vehicle.
Those skilled in the art know the operating principle of an AM, that is to say amplitude-modulated, radio signal received by a suitable radio receiver, with a view to being demodulated and then played to listeners.
One known problem relating to the reception of an AM radio signal via a mobile radio receiver, in particular one integrated into an electric or hybrid motor vehicle, resides in the fact that electromagnetic interference, in particular generated by the electric motor in the case of an electric or hybrid vehicle, perturbs the received AM radio signal.
As a result, filtering, typically achieved by means of an impulse response filter (“FIR”), is necessary in order to remove said electromagnetic interference.
With reference to FIG. 1, to remove the electromagnetic interference from a received AM radio signal, impulse response filters FIR have been developed. These filters implement CPA algorithms (described below) configured to attenuate, in the received AM radio signal, expressed in complex baseband and denoted yn, said electromagnetic interference, with a view to delivering a processed AM radio signal zn.
In the prior art, the algorithms for removing electromagnetic interference are generally of the constant-phase type, as mentioned above Specifically, the principle of amplitude modulation ensures that the emitted radio signal has a constant phase. Thus, computational algorithms, called CPAs, have been developed and those skilled in the art are constantly seeking to improve them, with for main constraint to ensure, after computation, a substantially constant phase in the radio signal filtered within the receiver.
CPA algorithms are iterative computational algorithms the objective of which is to determine the real and imaginary parts of the complex coefficients to be applied to the complex vector corresponding to the received AM radio signal, expressed in complex baseband, with a view to achieving a combination allowing the electromagnetic interference present in the AM radio signal to be attenuated.
From a mathematical point of view, the principle presented above, in which the characteristic complex coefficients of an impulse response filter are attributed to the signals, expressed in complex baseband, received on the one hand by an antenna of a radio receiver, corresponding to an AM radio signal to which electromagnetic interference generated by a source of interference, such as an electric vehicle motor for example, has become added, and on the other hand by a second antenna connected to said source of interference, such as the aforementioned electric motor, corresponding to said interference, with a view to forming a filtered radio signal to be played after said electromagnetic interference has been canceled out, is expressed as follows.
The filtered radio signal is written:
      z    n    =                    W        n        T            ⁢              Y        n              =                  [                                            w              _                                      1              ,              n                                ⁢                                          ⁢                                    w              _                                      2              ,              n                                      ]            ⁡              [                                                            y                                  1                  ,                  n                                                                                                        y                                  2                  ,                  n                                                                    ]            
where y1,n is the radio signal, in complex baseband, received by the antenna in question of the radio receiver, corresponding to the emitted AM radio signal perturbed by electromagnetic interference, and y2,n is the signal received by the antenna receiving the noise from the source of interference, in particular the electric motor of an electric or hybrid vehicle, and w1,n, w2,n are the complex coefficients attributed, via an impulse response filter FIR, to said received radio signal.
In the prior art, CPA algorithms are implemented to determine the complex vector Wn able to minimize the following cost function:JCPA=E{|zn−|zn∥2}
Moreover, in the prior art, the vector Wn of complex coefficients is considered to consist of linear complex numbers, said vector Wn having the following form:
      W    n    =      [                                                      a                              1                ,                n                                      +                          jb                              1                ,                n                                                                                                    a                              2                ,                n                                      +                          jb                              2                ,                n                                                          ]  
The components of this vector Wn of complex coefficients are independent of one another and the real and imaginary parts of each component are also.
The corresponding cost function may be decreased using the instantaneous gradient technique, in order to be written:
      ∇          J      CPA        =      μ    ×                  Y        n                                                    Y            n                                    2              ×          (                                    z            n                    -                                                z              n                                                  _            )      
where μ is a chosen constant allowing the speed with which the gradient converges to be set, depending on the desired convergence stability and rapidity.
The way in which the complex coefficients are updated is then expressed by the following formula:
      W          n      +      1        =            W      n        -          μ      ×                        Y          n                                                                Y              n                                            2                    ×              (                                            z              n                        -                                                        z                n                                                            _                )            
This algorithm, which is representative of the prior art, gives the curves of solutions in FIG. 2, with real part Re and imaginary part Im, and is liable to converge toward non-optimal solutions. In particular, although it is correct for the phase to converge toward 0, the curve of solutions of the prior art also allows the gain to converge toward 0, while being an objective solution for the CPA algorithm implemented.
To mitigate this major drawback, in the prior art, it is known to add a normalization coefficient to the updated equation of the complex coefficients to be implemented via an impulse response filter. Said update of the complex coefficients therefore becomes:
      W          n      +      1        =            (                        W          n                -                  μ          ×                                    Y              n                                                                                        Y                  n                                                            2                                ×                      (                                                            z                  n                                -                                                                        z                    n                                                                                _                        )                              )        ⁢          (              1        -        γ        +                  γ                                                                  W                n                                                    2                              )      
One major drawback of known filtering techniques and of CPA algorithms such as they are applied at the present time, with a view to removing the electromagnetic interference in particular produced by the electric motor of an electric or hybrid vehicle, resides in the fact that they sometimes converge slowly, and above all in the fact that they sometimes converge wrongly and have a poor stability. In other words, sometimes complex coefficients that meet the required conditions lead to a radio signal of poor quality being played.